Let’s try another that we need to factor.Problemy=x2−5x−14𝑦=𝑥2−5𝑥−14 SolutionList out the factors of −14−14:−1−1 and 141411 and 22 and −2−2 and Which of these pairs add up to −5−5? and Now we’ll write this in factored form:y=(x+𝑦=(𝑥+ )(x−)(𝑥− ))To find the zeros/solutions/x𝑥-intercepts, set each factor equal to 00 and solve for x𝑥.x+𝑥+ =0=0 and x−𝑥− =0=0x=𝑥= and x=𝑥= Our two solutions are (( ,, )) and (( ,, )) (Enter from least to greatest.)We can now use these to find the vertex. Remember the x𝑥-value of the vertex, as well as the axis of symmetry, is halfway between the two solutions.−2+72=52=2.5−2+72=52=2.5x=2.5𝑥=2.5 is our axis of symmetry. We’ll substitute this value into our original equation to find the y𝑦-value of the vertex.y=(𝑦=( )2−5()2−5( )−14)−14y=6.25−12.5−14𝑦=6.25−12.5−14y=−20.25𝑦=−20.25The vertex is (( ,, )).Finally, state the domain and range.Domain: All real numbers (as with all quadratic functions)Range: y≥𝑦≥ CheckQuestion 3
Question
Let’s try another that we need to factor.Problemy=x2−5x−14𝑦=𝑥2−5𝑥−14 SolutionList out the factors of −14−14:−1−1 and 141411 and 22 and −2−2 and Which of these pairs add up to −5−5? and Now we’ll write this in factored form:y=(x+𝑦=(𝑥+ )(x−)(𝑥− ))To find the zeros/solutions/x𝑥-intercepts, set each factor equal to 00 and solve for x𝑥.x+𝑥+ =0=0 and x−𝑥− =0=0x=𝑥= and x=𝑥= Our two solutions are (( ,, )) and (( ,, )) (Enter from least to greatest.)We can now use these to find the vertex. Remember the x𝑥-value of the vertex, as well as the axis of symmetry, is halfway between the two solutions.−2+72=52=2.5−2+72=52=2.5x=2.5𝑥=2.5 is our axis of symmetry. We’ll substitute this value into our original equation to find the y𝑦-value of the vertex.y=(𝑦=( )2−5()2−5( )−14)−14y=6.25−12.5−14𝑦=6.25−12.5−14y=−20.25𝑦=−20.25The vertex is (( ,, )).Finally, state the domain and range.Domain: All real numbers (as with all quadratic functions)Range: y≥𝑦≥ CheckQuestion 3
Solution
The problem seems to be incomplete. However, I can guide you through the steps of solving a quadratic equation of the form y = x^2 - 5x - 14.
Step 1: Factor the quadratic equation. The factors of -14 that add up to -5 are -7 and 2. So, the factored form of the equation is y = (x - 7)(x + 2).
Step 2: Find the zeros/solutions/x-intercepts. Set each factor equal to 0 and solve for x. x - 7 = 0 gives x = 7 and x + 2 = 0 gives x = -2. So, the solutions are x = -2 and x = 7.
Step 3: Find the vertex. The x-value of the vertex is halfway between the two solutions, which is (-2 + 7)/2 = 2.5. Substitute x = 2.5 into the original equation to find the y-value of the vertex. y = (2.5)^2 - 5*2.5 - 14 = -6.25. So, the vertex is (2.5, -6.25).
Step 4: State the domain and range. The domain of a quadratic function is all real numbers. The range is y ≥ -6.25 because the vertex is the minimum point of the parabola and its y-coordinate is -6.25.
Please provide the complete problem for a more accurate solution.
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